where \(z=\left(z^{(1)},\ldots ,z^{(n)}\right)^T \in \mathbb {R}^n\) . Here, every alternative \(i\)  belongs to exactly one nest \(N_\ell \subset \lbrace 1, \ldots , n\rbrace \)  for \(\ell = 1, \ldots , L\) . Compared to the well-known multinomial logit model with just one nest, the nested logit is more appropriate to model differentiated products. Nested logit allows in particular the violation of the axiom of irrelevance of independent alternatives, see e. g. [1]}.
The consumer surplus (REF ) is then
\(E(v) = \ln \left(\sum \limits _{l=1}^{L} \left(\sum \limits _{i \in N_\ell }^{} e^{v^{(i)} /\mu _\ell }\right)^{\mu _\ell }\right).\) 
